The differential equation of an arbitrary reflecting surface

被引：1

作者：

Melka, Richard F. ^{[1
]}

Berrettini, Vincent D. ^{[1
]}

Yousif, Hashim A. ^{[1
]}

机构：

[1] Univ Pittsburgh Bradford, Phys & Computat Sci Div, Bradford, PA 16701 USA

来源：

EUROPEAN JOURNAL OF PHYSICS | 2018年 / 39卷 / 03期

关键词：

geometrical optics; conic sections; nonlinear differential equations;

D O I：

10.1088/1361-6404/aaa8fc

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

A differential equation describing the reflection of a light ray incident upon an arbitrary reflecting surface is obtained using the law of reflection. The derived equation is written in terms of a parameter and the value of this parameter determines the nature of the reflecting surface. Under various parametric constraints, the solution of the differential equation leads to the various conic surfaces but is not generally solvable. In addition, the dynamics of the light reflections from the conic surfaces are executed in the Mathematica software. Our derivation is the converse of the traditional approach and our analysis assumes a relation between the object distance and the image distance. This leads to the differential equation of the reflecting surface.

引用

页数：7